mathematics for elementary teachers 7.3 ratios

Question

. A dough recipe calls for 3 cups of flour and 1

1

4

cups of water. You want to use the same ratio of

flour to water to make a dough with 10 cups of

flour. How much water should you use?

a. Solve this problem by setting up an equation

in which you set two fractions equal to each

other.

b. Interpret the two fractions that you set equal

to each other in part (a) in terms of the recipe.

Explain why it makes sense to set these two frac-tions equal to each other.

c. Why does it make sense to cross-multiply the

two fractions in part (a)? What is the logic

behind the procedure of cross-multiplying?

d. Now solve the problem of how much water to

use for 10 cups of flour in a different way, by

using the most elementary reasoning you can.

Explain your reasoning clearly

Answer 1

3 / 1.25 = 10 / f

3f = (1.25)(10), product means = product extremes

3f = 12.5

f = 4.167

Now how does one measure 0.167 of a cup?

Some insight from a baker.

0.5 cup = 8 tablespoons

8 tablespoons = 24 teaspoons

1 / 3 of 24 teaspoonss is 8 teaspoons, or 2 tablespoons and 2 teaspoons.